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Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes. (English) Zbl 0936.60037
The author extends forward-backward martingale decomposition of Meyer-Zheng-Lyons’s type from the symmetric case to the general stationary situation for the partial sum \(S.(f)\) with \(f\) satisfying a finite energy condition. Furthermore, as corollaries, he obtains a maximal inequality and a tightness result related to the functional central limit and a criterion of a.s. compactness related to the functional law of iterated logarithm.

MSC:
60F17 Functional limit theorems; invariance principles
60J55 Local time and additive functionals
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